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4

You could compute index dividend yield from ATM options using linearized put-call parity (assuming index options are European.) The present value of the dividend payment is: $PV(div) = P - C + (S - K) + K(e^{rT} - 1)$ where $r$ is interest rate to the option expiration and $T$ is time to maturity in years. Then the implied dividend is: $d = ...


3

I found that sometimes going back to the source gets me the farthest. Here is what you are probably looking for: http://www.math.ku.dk/kurser/2005-1/finmathtowork/ODD.pdf Discrete dividends that have not been declared yet need to be estimated. Estimating and updating dividend expectations is part of the job of every single stock vol trader. You are asking ...


2

The derivation in the book appears wrong. However, the results make sense as the option price at time $t$ should not be impacted by prior dividend payments. It may be out-of topic, I would like to provide some justification of the Musiela-Rutkowski formula. Let $\{H_t \mid t >0\}$, where \begin{align*} H_t = \sum_{0 < T_i \leq t} q_i, \end{align*} ...



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